Lost sinners have free will remaining to reject, but do they have any to choose Jesus as Lord and Savior?
God would disagree with that.
God calls lost sinners to repentance
1] through creation Rom_1:20
2] the conviction of the Holy Spirit Joh_16:8-9
3] the gospel message Rom_1:16
4] observing Christians lives 1Pe_2:12
So unless you think God is is a liar then He must think that man can hear and believe the gospel message and turn to Him in faith.
Act 16:30 and after he brought them out, he said, "
Sirs, what must I do to be saved?"
Act 16:31 They said, "
Believe in the Lord Jesus, and you will be saved, you and your household."
By your logic Paul should have told him there is nothing you can do and you could not even really ask that question as you would never want to be saved. Which then begs the question of why Paul even preached the gospel message at all?